A radiation detector of this kind is known from U.S. Pat. No. 4,213,055. Therein, radiation detector in the form of an X-ray image intensifier tube comprises an entrance screen which is provided on a metal support and comprises a luminescent material and a photocathode. In a tube of this kind an image-carrying beam of photoelectrons is imaged on an exit screen which comprises a phosphor layer for conversion of the photoelectrons into light. The electron-optical system in a tube of this kind is adapted to form an optimum image of the image-carrying beam of photoelectrons on an exit screen.